MISION

This subsection presents the results of analysing the error in the kinematic distance method using the actual cloud velocities from the simulation. These include net radial and azimuthal streaming, which appear as an average shift of the cloud velocity distribution with respect to a circular orbit.

Section I

Figure 5.10 (left panel) plots the kinematic distance with respect to the actual distance for the clouds in this section, which corresponds to the actual region of the simulation. The results show that the distance is overestimated for almost all clouds. The upper right panel of Figure 5.11 shows the histogram of distance errors, which has a systematic offset of _≈ 1 kpc. The error falls between −1 and 2 kpc. Approximately 87% of the clouds have a distance error within 0.5 and 1.5 kpc. In terms of a fractional error, the error ranges between ₋5% and 16%. The systematic offset towards an overestimated distance may be a consequence of the net inward radial motion of the cloud distribution. In this line-of-sight, the radial component

v_R has a larger contribution to v_los and opposite to the projection of v_φ. This results in a

lower line-of-sight velocity compared to that expected from a circular orbit which results in an overestimated distance asv_cat a further distance would match the measuredv_los.

Section II

The results for this section are plotted in the left panel in Figure 5.10, which shows that the kinematic method is overestimating the distance for most of the cloud distribution. The dis-

5.4. Error Analysis of the Kinematic Distance

Figure 5.9:Cloud positions recovered from the kinematic distance. The clouds were assigned a velocity corresponding to the local circular velocity plus a component from a cloud-to-cloud velocity dispersion symmetric with respect to the rotation curve. The top panel shows the case forσ_R=10 km s−1and

tance grows with a decreasing actual distance. The error histogram (left panel of Figure 5.11) has a noticeable peak around 2 kpc and a smaller peak near 0.7 kpc. The distribution is ap- proximately centred around 1 kpc, also showing a net systematic shift towards overestimated distances. The max/min error range is ₋1.0/3.0 kpc. There are a few outliers with errors

close to₋2 kpc. Approximately 38% of the clouds have errors within 0.5 and 1.5 kpc. This includes the smaller peak of the distribution. About 34% off the clouds are in the range be- tween 1.5 and 2.5 kpc, which includes the larger peak. This shows that around 75% have errors between 0.5 and 2.5 kpc. A fraction of 23% falls between₋0.5 and 0.5 kpc. In terms of a fractional error, the distribution ranges from₋58% to 80%. This arm section is located in a point where the contribution of v_Rto the v_los is very low and the projection ofvφis very

high. The cloud distribution has an average azimuthal velocity slower than the rotation curve, which explains the overall shift of the distribution. The two velocity groups in the azimuthal component explains the bimodality of the distribution.

Section III

In this region, the error in the distance appears to increase as the actual distance falls. The results are shown in the right panel of Figure 5.10. The error distribution also bimodal and has two peaks, one near 1 kpc and another around₋0.5 kpc, as shown in the lower left panel of Figure 5.11. Around 41% of the clouds has errors within−1 kpc and 0 kpc, where one peak is located. Between 1 kpc and 2 kpc, the fraction drops to about 27%, this is where the second peak is located. A similar value is found in the range between 0 and 1 kpc. The fractional error ranges from₋28% and 39%. For this section, most of the errors have negative values. The bimodal distribution is a consequence of the two groups in circular velocity.

Section IV

The results for this section are shown in the right panel of Figure 5.10. The error grows with increasing cloud distance. In the error histogram of Figure 5.11 (lower right panel), the distribution shows a systematic offset of _≈ 1 kpc. The error ranges from ₋2 kpc to 4kpc.

Approximately 58% of the clouds have an error within ₋1.5 and₋0.5 kpc. About 34% falls within the range between −0.5 kpc and 1 kpc. The fractional error falls within −13% to 27%. For this region, v_R<0 which makes the projection ofvφandvRcontribute in the same

5.4. Error Analysis of the Kinematic Distance

Figure 5.10:Cloud kinematic distanceDkincompared to the actual valueDactualfor an azimuthal scatter

around the galaxy’s circular velocity ofσ_φ=10 km s−1. Sections I and II are shown in the left panel.

Sections III and IV are shown in the right panel.

the one expected from a circular orbit. A more negative line-of-sight velocity results in an underestimated distance when using the kinematic estimate because a circular orbit would have to lie at a smaller radius to match the projected velocity. This explains the negative systematic shift of the error distribution.

Recovered Positions

The cloud positions that an imaginary observer would recover from the kinematic distance are plotted in Figure 5.12. These are compared with the original cloud distribution in each region. The orange curves plot the spiral arm curves tracing the actual cloud regions.

In section I, the systematic shift towards overestimated distance results in a recovered distribution at a farther distance compared to the original one. In the spiral of section II, the distribution has an overall shift towards overestimated distances as well. This reflects in an apparent net shift of the centre of the cloud distribution and an artificial increase in its size along the line of sight. A similar effect is observed for section III. In the case of section IV, there is a significant distortion of the geometry of the recovered cloud distribution. However, the behaviour is different to the case of section I. Although most of the clouds of section IV are shifted towards smaller distances, there is still a fraction with overestimated values.

The results of this section shows that average radial and azimuthal deviations from a cir- cular orbit in a group of clouds introduces systematic errors in the kinematic distance. For the values found in the simulation, these can be as large as 1 kpc. This effect was not found in §5.4.1, where the cloud velocity distribution was assumed to be symmetric around the circular

−4 −3 −2 −1 0 1 2 3 4 D_kin −Dactual[kpc] 0 50 100 150 200 250 N II −4 −3 −2 −1 0 1 2 3 4 D_kin −Dactual[kpc] 0 50 100 150 200 250 300 350 N I −4 −3 −2 −1 0 1 2 3 4 D_kin −Dactual[kpc] 0 20 40 60 80 100 120 140 160 N III −4 −3 −2 −1 0 1 2 3 4 D_kin −Dactual[kpc] 0 50 100 150 200 250 300 350 N IV

Figure 5.11: Distance error(Dkin−Dactual)distributions per section: section I (upper right), section II

(upper left), section III (lower left), section IV (lower right). These are results from the kinematics in the actual simulation, which include both radial and azimuthal streaming motions. The net offset in the distribution of sections I and IV is a consequence of a net inward radial motion and the bimodal behaviour in sections II and III is a result of the two main groups in the azimuthal velocity.

5.4. Error Analysis of the Kinematic Distance

Figure 5.12: Recovered positions maps colour coded by the cloud’s azimuthal velocity from the simu- lation. The solid curves represent the spiral arms tracking the actual cloud distribution. These results show the error introduced by streaming motions in the spiral arm in the recovered positions obtained using the kinematic distance.

velocity. The cloud-to-cloud dispersion propagates into a broader error distribution around the systematic shift.